question_answer

At time t = 0 magnetic field of 1000 Gauss is passing perpendicularly through the area defined by the closed loop shown in the figure. If the magnetic field reduces linearly to 500 Gauss, in the next 5 s, then induced EMF in the loop is                                                                                        [JEE MAIN Held On 08-01-2020 Morning]

A) \[48\,\mu V\]     

B) \[36\text{ }\mu V\]

C) \[56\text{ }\mu V\]        

D) \[28\text{ }\mu V\]

Correct Answer: C

Solution :

[c] Using faraday law Induced EMF \[=\left| -\frac{d\phi }{dt} \right|=\left| A\frac{dB}{dt} \right|\] \[\therefore \frac{dB}{dt}=\frac{1000-500}{5}\times {{10}^{-4}}={{10}^{-2}}T/\sec \] Area \[=\left( 16\times 42\times Area\text{ }of\text{ }triangle \right)c{{m}^{2}}\] \[=\left( 64-2\times \frac{1}{2}\times 2\times 4 \right)c{{m}^{2}}\] \[=56\times 104{{m}^{2}}\] \[\therefore {{\varepsilon }_{induced}}=56\times {{10}^{6}}\text{ }V=56\text{ }\mu V\]